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LIMITS AND DERIVATIVES — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSLIMITS AND DERIVATIVES2 Marks
Question
Find the derivative of. $(5\text{x}^3+3\text{x}-1)(\text{x}-1)$
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Answer

Let $\text{f}(\text{x})=(5\text{x}^3+3\text{x}-1)(\text{x}-1)$ By Leibnitz product rule, $\text{f}'(\text{x})=(5\text{x}^3+3\text{x}-1)\frac{\text{d}}{\text{dx}}(\text{x}-1)+(\text{x}-1)\frac{\text{d}}{\text{dx}}(5\text{x}^3+3\text{x}-1)$ $=(5\text{x}^3+3\text{x}-1)(1)+(\text{x}-1)(5.3\text{x}^2+3\text{x}-0)$ $=(5\text{x}^3+3\text{x}-1)+(\text{x}-1)(15\text{x}^2+3)$ $=5\text{x}^3+3\text{x}-1+15\text{x}^3+3\text{x}-15\text{x}^2-3$ $=20\text{x}^3-15\text{x}^2+6\text{x}-4$

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